Find the foot of the perpendicular from the point `(0,2,3)` on the line `(x+3)/5=(y-1)/2=(z+4)/3dot` Also, find the length of the perpendicular.

Explanation

To find the foot of the perpendicular from the point \( P(0, 2, 3) \) to the line given by the equations \( \frac{x+3}{5} = \frac{y-1}{2} = \frac{z+4}{3} \), we can follow these steps:

### Step 1: Parametrize the line
The line can be expressed in parametric form. Let \( \lambda \) be the parameter. From the given equation, we can write:
- \( x = 5\lambda - 3 \)
- \( y = 2\lambda + 1 \)
- \( z = 3\lambda - 4 \)

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